Just to be accurate, here is a chart with all the storage levels:
In terms of gigabytes, which I am sorta using as a 'standard' here is the equilvalents.
1 Terabyte=1024 gigabytes.
1 Petabyte=1048576 gigabytes.
1 Exabyte=1,073,741,824 gigabytes.
(Gets interesting names from here)
1 Zettabyte=1,099,511,627,776 (1 TRILLION+) Gigabytes
1 Yottabyte=1,125,899,906,842,624 (1 quadrillion+)gigabytes. (or over 1 quintillion megabytes)
Now you are REALLY REALLY REALLY a hardcore nerd if you even come close to needing a Yottabyte. You could probably store every movie, music, picture, etc. on the internet with just one or two Yottabytes and maybe have room to spare(I hope everyone can agree on that

).
Just running it through a calc, you can have over 1 TRILLION hours of movies to just use 1 yottabyte. You would have to live for 100 million +years just to watch it all. Or you could have over 2 trillion hours of music. For that you would have to live for 200 million years.
Even if you did somehow in a freaky way filled up an entire yottabyte, how would you even keep track of how many files that would be.
BTW: I had to google what the name of the digits past a trillion are

I also appears like they were running short of cool names past a exabyte

Here is the american digit system:
thousand
million
billion
trillion
quadrillion
quintillion
sextillion
septillion
octillion
nonillion
decillion